Partial data inverse problems for quasilinear conductivity equations

Abstract

We show that the knowledge of the Dirichlet-to-Neumann maps given on an arbitrary open non-empty portion of the boundary of a smooth domain in $${\mathbb {R}}^n$$ , $$n\ge 2$$ , for classes of semilinear and quasilinear conductivity equations, determines the nonlinear conductivities uniquely. The main ingredient in the proof is a certain $$L^1$$ -density result involving sums of products of gradients of harmonic functions which vanish on a closed proper subset of the boundary.